Sum and product related theorems of entire function in terms of (α,β,γ)-order
Biswas, C., Das, B., Pal, S. (2025). Sum and product related theorems of entire function in terms of (α,β,γ)-order. EKB Journal Management System, 16(1), 1-6. doi: 10.21608/jfca.2025.317726.1130
Chinmay Biswas; Bablu Chandra Das; Sudipta Kumar Pal. "Sum and product related theorems of entire function in terms of (α,β,γ)-order". EKB Journal Management System, 16, 1, 2025, 1-6. doi: 10.21608/jfca.2025.317726.1130
Biswas, C., Das, B., Pal, S. (2025). 'Sum and product related theorems of entire function in terms of (α,β,γ)-order', EKB Journal Management System, 16(1), pp. 1-6. doi: 10.21608/jfca.2025.317726.1130
Biswas, C., Das, B., Pal, S. Sum and product related theorems of entire function in terms of (α,β,γ)-order. EKB Journal Management System, 2025; 16(1): 1-6. doi: 10.21608/jfca.2025.317726.1130

Sum and product related theorems of entire function in terms of (α,β,γ)-order

Journal of Fractional Calculus and Applications
Volume 16, Issue 1, 2025, Page 1-6  XML PDF (181.4 K)
Document Type: Regular research papers
DOI: 10.21608/jfca.2025.317726.1130
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Authors
Chinmay Biswas email 1; Bablu Chandra Das1; Sudipta Kumar Pal2
1Department of Mathematics, Nabadwip Vidyasagar College, Nabadwip, Dist.- Nadia, PIN-741302, West Bengal, India.
2Department of Mathematics, Jangipur College, P.O.-Jangipur, Dist.-Murshidabad, PIN-742213, West Bengal, India.
Abstract
Growth analysis of entire and meromorphic function is a very important part in complex analysis. Order is a classical growth indicator of entire and meromorphic functions. During the past several years, many renowned Mathematicians have made the close investigations on the properties of
entire and meromorphic functions in different directions using the concepts of order and some extended definitions of order, like iterated $p$-order [7, 8], $(p,q)$-th order [5, 6], $(p,q)$-$\varphi $ order [9], $\varphi $-order [3] etc.\ and they have achieved many valuable results. Heittokangas et al. [4] have introduced another the concept of $\varphi $-order of entire and meromorphic functions considering $\varphi $ as subadditive function. Later, Bela\"{\i}di et al. [1] have extended the above ideas and have introduced the definitions of $(\alpha ,\beta,\gamma )$-order and\ $(\alpha ,\beta ,\gamma )$-lower order of entire and meromorphic functions. In this paper, we investigate some basic properties in connection with sum and product of $(\alpha ,\beta ,\gamma )$-order and\ $(\alpha ,\beta ,\gamma )$-lower order of entire function with respect to another entire function where $\alpha ,\beta ,\gamma $ are continuous non-negative functions defined on $(-\infty ,+\infty )$ with $\alpha \in L_{1}$, $\beta \in L_{2}$, $\gamma \in L_{3}$.
Keywords
Growth; Property (A); (α; β; γ)-order
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